The complete set of symmetry operators of the schrödinger equation

The complete set of symmetry operators of an arbitrary order associated with the Schrödinger equation is found. It is shown that this equation is invariant with respect to a 28-dimensional Lie algebra, realized in the class of differential operators of the second order. Higher-order symmetries of the Levi-Leblond equation are investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 11, pp. 1521–1526, November, 1991.     

Chernoff efficiency of the sign and Wilcoxon tests for testing the symmetry hypothesis

The local Chernoff efficiency of the sign and Wilcoxon statistics are derived for the testing of symmetry on the basis of the analysis of the probabilities of large deviations of these statistics under the hypothesis and the alternative.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 101–107, 1989.     

Structure and reactivity of 2-methyl-9-hydroxy-4H-pyrido[1,2-a]pyrimidin-4-one

It has been shown that the alkylation of 2-methyl-9-hydroxy-4H-pyrido[1,2-a]pyrimidin-4-one takes place at the oxygen atom, but electrophilic substitution takes place mainly at position 8 of the molecule (the ortho position relative to the hydroxy group).Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1660–1666, December, 1992.     

Similar quartz crystallographic textures in rocks of continental earth’s crust (by neutron diffraction data): II. Quartz textures in monophase rocks

The types of quartz textures found in a large collection of multiphase rocks from different regions of the earth are analyzed. Crystallographic textures of granulite, amphibolite, slate, and gneiss samples are measured, classified, and compared with the similar textures of monomineral rocks.     

Onset of detonation in polydispersed fuel–air mixtures

Investigations of detonation onset in pulverized fuel–air mixtures were carried out. Combustion and detonation processes in sprays differ greatly from that in homogeneous mixtures, because not only chemical reactions, but physical processes of combustible mixture formation take place within the combustion zone (droplets atomization and evaporation). The polydispersed character of mixture and non-uniformity of droplet spatial distribution strongly affects spray combustion and detonation onset. The present paper contains the results of theoretical and experimental investigations of detonation onset peculiarities in polydispersed non-uniform hydrocarbon–air mixtures.     

Electrochemically induced processes in the formation of phosphorus acid derivatives. 2. The role of polymerization processes in the electrosynthesis of the esters of phosphorus acids from white phosphorus

The mechanism of the electrosynthesis of phosphate esters from white phosphorus was investigated. It was shown that the reaction takes place by two paths, i.e., monomeric (with the participation of dissolved phosphorus) and polymeric (with the participation of phosphorus on the surface of an emulsion drop). It was established that in an alcohol solution of tetraethylammonium iodide the main part of the final product is formed through an intermediate polymeric compound. It was noticed that by studying the dynamics of the accumulation of the dissolved product during electrolysis it is possible to trace the mechanism of reaction of the phosphorus at the individual stages of the process.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan' Scientific Center, Russian Academy of Sciences, 420028 Kazan'. V. I. Ul'yanov-Lenin Kazan' State University, 420028 Kazan'. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 6, pp. 1328–1333, June, 1992.     

Bahadur effectiveness of Watson-Darling goodness-of-fit tests

The rough asymptotic behavior of the probability of large deviations is found for Watson-Darling goodness-of-fit tests, which are centered versions of Kolomogorov-Smirnov statistics. Their Bahadur effectiveness is calculated and conditions for local asymptotic optimality for the alternative of translation are studied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 138–145, 1987.     

Electron diffraction study of the molecular structure of gaseous 1,1-dibromo-3,3,5,5-tetramethyl-1-stanna-3,5-disila-4-oxacyclohexane,Br2Sn(CH2SiMe2)2O

The molecular structure of gaseous Br₂Sn(CH₂SiMe₂)₂O was studied by electron diffraction. The six-membered ring has a chair conformation whereas the entire molecule possessesC _s symmetry. The existence of a boat conformer cannot be completely excluded. The results of theoretical calculations for a twisted-boat conformation are at variance with the experimental data. Steric strain caused by mutual repulsion of the two axial methyl groups is reduced to the tilt of the Me₂Si fragments in opposite directions. This results in an increase (up to 26°C) in the angle formed by the bisector of the C_M-Si-C_M angle with the C_cSiO plane. The main geometrical parameters are as follows:r _g (Å): Si-O 1.708(20); Si-C_M 1.862(20); Si-C_c 1.882(9); Sn-C 2.108(26); Sn-Br 2.456(3); C-H 1.099(30); (degr.): C-Sn-C 105(2); Br-Sn-Br 107.9(1.2); Si-O-Si 129.6(3); C_M-Si-C_M 112; Si-C-H 113 (fixed value in accordance with experiment); C_c-Si-O 107(2); Sn-C-Si 109(2); torsion angles: (Si-C) 52(2); (Si-O) 62(1); (C_c-Sn) 54(1). The average amplitudes were fixed at the values calculated from the force field. Structural parameters of molecules with similar structures were analyzed and compared.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 384–387, February, 1993.     

Chiral methylbenzylammonium salts of aryldithiophosphonic acids containing glucofuranose,allofuranose, and galactopyranose diacetonide scaffolds

Abstract

New chiral methylbenzylammonium salts of aryldithiophosphonic acids containing glucofuranose, allofuranose, and galactopyranose diacetonide substituents were obtained using (S)-(–)-α-methylbenzylamine, (R)-(+)-α-methylbenzylamine, and (R,S)-(±)-α-methylbenzylamine. Salts obtained possess antimicrobial activity.